Let \(T>0\)  be a real number and \((X,\Vert \cdot  \Vert _{X})\)  a normed space, where \(X\)  can be either \(L^{2}(\Omega )\)  or \(H^{s}(\Omega )\) , \(s\ge 0\) .
According to [1]}, the Bochner space \(L^{p}(0,T;X)\)  is
the space of functions \(v\)  such that the sublinear functional
\(\Vert v \Vert _{L^{p}(0,T;X)}= {\left\lbrace \begin{array}{ll}\displaystyle \left(\int _{0}^{T}\Vert v(t) \Vert _{X}^{p}\,dt\right)^{1\slash {p}} & 1\le p<\infty ,\\\textrm {ess sup}_{t\in [0,T]}\Vert v(t) \Vert _{X} & p=\infty ,\end{array}\right.}\) 
